England - Germany (2-0)
Raheem Sterling and Harry Kane scored in the final 15 minutes to earn Gareth Southgate's men a last-eight berth.
England matched Germany's 3-5-2 formation and the sides cancelled each other out for much of the first half. The Three Lions had the first efforts of note with Raheem Sterling testing Manuel Neuer from distance and Harry Maguire heading Kieran Trippier's cross wide. The Mannschaft prised the best opening of the first 45 minutes, though, only for Jordan Pickford to thwart Timo Werner.
The England No1's agility came to the fore with a fine tip over from Kai Havertz after the break and Gareth Southgate's team took advantage with 15 minutes to play, Sterling slotting in emphatically after Harry Kane and Jack Grealish had worked Luke Shaw into a crossing position down the left.
Thomas Müller dragged his effort wide when one on one against Pickford, and that miss was magnified when Kane stooped to head home Grealish's cross and condemn Joachim Löw to defeat in his final game at the Germany helm.
England vs Ukraine, Rome, Saturday 3 July
Sweden - Ukraine (1-2)
Artem Dovbyk's first international goal took Ukraine into a first EURO quarter-final, the substitute heading in during the final seconds of extra time to see off ten-man Sweden at Hampden Park.
Both sides started brightly in Glasgow, Roman Yaremchuk's early shot kept out by Sweden goalkeeper Robin Olsen while at the other end, Alexander Isak curled a shot a metre wide. Ukraine, in their first EURO knockout game, struck first in the 27th minute, Andriy Yarmolenko working the ball on to his left foot and curling a sumptuous pass with the outside of his boot for Oleksandr Zinchenko to hammer a shot past Olsen.
Sweden responded positively to falling behind, and were back on terms two minutes before the break. Isak found Emil Forsberg just outside the area and his well-struck shot deflected off Illia Zabarnyi on its way past Georgiy Bushchan.
The second half was similarly open, Serhiy Sydorchuk's shot clipping the outside of the post; seconds later, Isak played in Forsberg for a shot that also rattled the upright. The Sweden midfielder then smashed an effort against the crossbar, but neither team could conjure a winner as this round of 16 tussle headed to extra time.
Sweden lost Marcus Danielson to a red card for a challenge on Artem Besedin in the first additional period, and just when it looked like penalties were inevitable, Ukraine upped the tempo. They got their reward a minute into added time, Zinchenko's pinpoint cross headed in by substitute Dovbyk to spark wild celebrations.
Ukraine – vs England in Rome, Saturday 3 July